Aircraft: SMALL AIRCRAFT; HIGH WING; 1 ENG; FIXED GEAR
Phase of flight: Initial Climb
Anomaly: Aircraft Equipment Problem Critical; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Incursion Runway; Inflight Event / Encounter Aircraft

In the upwind after VFR departure; Aircraft X advised that he wanted to return to the field. I immediately asked if he needed any help and he replied no. I told him to make left traffic. As he didn't indicate an [urgent problem]; I treated him like a regular aircraft who decided to return to the field. We get this all the time for all sorts of reasons. It was nothing out of the ordinary at that point. He was going to be next to land just as soon as I departed the waiting IFR Aircraft Y. In order to depart Aircraft Y I had to first turn two pattern aircraft out of the way early. As soon as the second aircraft - a touch-and-go aircraft- passed the threshold; I told Aircraft Y to LUAW (Line Up and Wait); which he read back and did. I informed Aircraft X (who at this point was approaching the midfield left downwind) that I would give him a base turn and landing in just a moment as traffic was in position. He again acknowledged without issue. I then told the first aircraft (a stop-and-go aircraft) to turn an early left crosswind when able and waited to tell the second aircraft (a touch-and-go aircraft) the same once he was safely established in the upwind. At that point; Aircraft X suddenly announced that he was turning base right now and had to land. I acknowledged the base turn and immediately told the upwind [touch-and-go aircraft] to start his early crosswind now; which he did and then went right to the Aircraft Y and cleared him for 'immediate' takeoff; which he didn't even acknowledge. I asked Aircraft Y if he'd started his roll; knowing Aircraft X was essentially now in a short approach. The Aircraft Y responded by saying he was 'holding position.' At this point I knew he hadn't been paying attention and there was no moving him out of the way in time. I told Aircraft Y to cancel his takeoff clearance and hold in position because any movement would have increased the likelihood of his being in the way of the inbound behind him. He acknowledged; 'hold position.' I then went right to Aircraft X and advised that I couldn't give a landing clearance because traffic was on the runway. He acknowledged but repeated that he had engine trouble and was coming in to land. I gave him the traffic on the runway and informed him that Aircraft Y wasn't moving. He responded that he would side-step around the jet and land in front of it. I repeated again to Aircraft Y to hold position and informed the pilot what was happening to help his situational awareness; telling him that a 'Aircraft X' would be coming around to land on the runway in front of him. He acknowledged and didn't move. Aircraft X landed without further incident and rolled out to the taxiway exit where he was taxied by Ground Control and met by Operations vehicles. If a pilot's aircraft indicates any sort of malfunction whatsoever on takeoff that prompts a request to return to the field; it should be required that the controller be made aware of this for priority and for a sterile runway. Otherwise we will just fit them right back into the pattern and treat them as any other inbound. This return to the field is a very common occurrence for all sorts of [non-priority] reasons. Barriers which might serve to deter pilots from declaring [urgency] or requesting priority should be removed so they can feel free to request the help they might need without repercussions. Additionally; changes should be made on both the controller and pilot sides in the event neither has time to [advise ATC]. When seconds allow for only the transmission of control instruction to prevent collision; neither party should be held liable for not having wasted precious time saying pointless words in that moment. The actions being taken alone speak to the [situation] without having to necessarily say as much. Tower Controller reported a departing aircraft had to return to the airport with an equipment problem. Aircraft landed over traffic that was in position and holding on the runway.